(SEM IV) THEORY EXAMINATION 2024-25 SIGNAL SYSTEM

This document contains the full B.Tech (Semester IV) Theory Examination 2024–25 question paper for Signal System (BEC403). The paper spans two printed pages, carries 70 marks, and evaluates a student's understanding of continuous-time and discrete-time signals, system properties, LTI system analysis, Fourier and Laplace transforms, Z-transform concepts, sampling, convolution, and stability of systems.

Section A – Short Conceptual Questions (14 Marks)

Section A presents seven 2-mark questions, covering core signal and system principles:

Definition and examples of energy and power signals (Page 1)

Key properties of linear systems

Meaning and role of convolution in LTI system analysis

Comparison of Fourier Series vs Fourier Transform

Definition of Region of Convergence (ROC) in Z-transform

Explanation of aliasing in sampling

Concept of eigenfunctions of LSI systems

These questions validate conceptual clarity in the basics of signal processing.

Section B – Analytical & Medium-Difficulty Problems (21 Marks)

Students answer any three of five questions. Topics include:

Even & Odd Signal Decomposition

Finding even and odd parts of
x(t) = cos(t) + sin(t) + cos(t)·sin(t)

Impulse Response of LTI System

Solving differential equation
dy/dt + 2y(t) = x(t)

Convolution via Fourier Transform

Convolving:

x₁(t) = e⁻⁴ᵗ u(t)

x₂(t) = e⁻⁸ᵗ u(t)

Time-Shifting & Frequency-Shifting in Z-Transform

Derivation + examples (Page 1)

Signal Reconstruction

Explanation of interpolation technique for reconstructing signals from samples

These questions check analytical skills and mathematical application.
 

Section C – Long, Higher-Order Problems (35 Marks)

Section C contains five questions (Q3–Q7), each with two choices, requiring deeper understanding.

Q3 – System Testing / Signal Classification

Testing linearity, time-invariance, and causality of:
y(t) = t · x(t)

OR determining whether x(t) = e⁻⁵ᵗu(t) is an energy or power signal (Page 1)

Q4 – Convolution Integral / Stability Analysis

Compute convolution of e⁻³ᵗu(t) with u(t)

OR find step response of h(t) = e⁻⁶ᵗu(t) and check BIBO stability (Page 2)

Q5 – Inverse Laplace / DTFT Analysis

Inverse Laplace of
X(s) = 2 / ((s+4)(s−1)) with ROC: −4 < Re(s) < 1

OR DTFT of
x(n) = 0.5ⁿu(n) + 2⁻ⁿu(−n−1)

Q6 – Z-transform & ROC / Inverse Z-transform

Z-transform of sin(ω₀n)u(n) with ROC

OR inverse Z-transform of
H(z) = 0.2z / [(z + 0.4)(z − 0.2)] with ROC: |z| > 0.4

Q7 – Sampling Theorem / Aliasing

Statement & proof of Sampling Theorem and effect of undersampling

OR determining aliasing for
x(t) = cos(500πt) + sin(700πt)
sampled at 400 Hz

These questions test deep conceptual knowledge, mathematical handling, and system behavior analysis.

Summary

The Signal System (BEC403) exam paper comprehensively evaluates:

Continuous & discrete signals

Energy vs power classification

LTI systems & convolution

Fourier Transform & Fourier Series

Z-transform & Laplace transform

Sampling theorem & aliasing

Stability, causality, linearity & time-invariance

DTFT and inverse Z-transform concepts

System responses (impulse & step)

This is a complete academic resource for students studying the fundamentals of signal and system analysis in electronics and communication engineering.